Usually Vannevar Bush's idea of the Memex is credited as the earliest concrete envisioning of the Web. But an article on Boxes and Arrows suggests an earlier example, namely that of Belgian man of letters Paul Otlet who envisioned a device remarkably similar to the Memex - but in 1934, years before publication of "As We May Think" in 1945.
One has to be careful in these claims though. First of all - Bush's Memex is more important, since it was a direct influence on later inventions of hypertext and not just a similar idea. Secondly, one shouldn't get too carried a way. The notion of 'universal systems' and classification is much older. Immediate forefathers may be found in the works of the Enlightenment. In fact during the Enlightenment it was the central concept. The Encyclopédie of Diderot is an attempt to construct such a 'universal book', Leibniz dreamed of languages of universals to describe all knowledge and automated discovery of new ideas, and Carl vno Linné founded the study of taxonomy.
You can look further, back to Greek philosophy and imperial inventories of Egypt and China. The urge to classify, collect and compare runs very deep.